2/12/08
to find the zero-state response of an LTID syste, we must know the response due to an impulse: delta(n) -> system -> impulse response
when the system is excided by a delta function, input is 0 for n>0
syste can only sustain a linear combinationi of the eigenfunctions of the system
therefore, the impuse response must be composed of eigenfunctions and a possible delta function at n=0
(Fig1)
can solve recursively
example (Fig2)

zero-state response
response of system due to input x when all initial conditions are 0
due to superposition, response of several impulses simply their sum
if we restrict ourselves to causal inputs and systems, we may make the following simplification to the convolution sum:
if an input x(n) is causal, then x(m)
table: (Fig3)
ex: (Fig4)
convolution by sliding tape method: (Fig5)
visual convolution with discrete data....

total response of system can be written as zero-in+zero-state
consider following diff equation: (Fig6)